Properties

Label 637.2.x.b.215.2
Level $637$
Weight $2$
Character 637.215
Analytic conductor $5.086$
Analytic rank $0$
Dimension $32$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 637 = 7^{2} \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 637.x (of order \(12\), degree \(4\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(5.08647060876\)
Analytic rank: \(0\)
Dimension: \(32\)
Relative dimension: \(8\) over \(\Q(\zeta_{12})\)
Twist minimal: no (minimal twist has level 91)
Sato-Tate group: $\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label 215.2
Character \(\chi\) \(=\) 637.215
Dual form 637.2.x.b.80.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.433802 + 1.61897i) q^{2} +0.637748i q^{3} +(-0.700831 - 0.404625i) q^{4} +(0.520288 + 1.94174i) q^{5} +(-1.03250 - 0.276656i) q^{6} +(-1.41124 + 1.41124i) q^{8} +2.59328 q^{9} +O(q^{10})\) \(q+(-0.433802 + 1.61897i) q^{2} +0.637748i q^{3} +(-0.700831 - 0.404625i) q^{4} +(0.520288 + 1.94174i) q^{5} +(-1.03250 - 0.276656i) q^{6} +(-1.41124 + 1.41124i) q^{8} +2.59328 q^{9} -3.36932 q^{10} +(0.694217 - 0.694217i) q^{11} +(0.258049 - 0.446954i) q^{12} +(1.60977 + 3.22624i) q^{13} +(-1.23834 + 0.331813i) q^{15} +(-2.48181 - 4.29862i) q^{16} +(-2.99281 + 5.18370i) q^{17} +(-1.12497 + 4.19844i) q^{18} +(1.98532 - 1.98532i) q^{19} +(0.421043 - 1.57135i) q^{20} +(0.822765 + 1.42507i) q^{22} +(-2.58851 + 1.49448i) q^{23} +(-0.900016 - 0.900016i) q^{24} +(0.830467 - 0.479471i) q^{25} +(-5.92151 + 1.20663i) q^{26} +3.56710i q^{27} +(3.65708 - 6.33425i) q^{29} -2.14878i q^{30} +(-8.34708 - 2.23659i) q^{31} +(4.18037 - 1.12013i) q^{32} +(0.442736 + 0.442736i) q^{33} +(-7.09397 - 7.09397i) q^{34} +(-1.81745 - 1.04931i) q^{36} +(4.63309 + 1.24143i) q^{37} +(2.35294 + 4.07541i) q^{38} +(-2.05753 + 1.02663i) q^{39} +(-3.47451 - 2.00601i) q^{40} +(0.886060 + 3.30682i) q^{41} +(-0.748633 + 0.432224i) q^{43} +(-0.767427 + 0.205631i) q^{44} +(1.34925 + 5.03547i) q^{45} +(-1.29661 - 4.83903i) q^{46} +(-2.96429 + 0.794280i) q^{47} +(2.74144 - 1.58277i) q^{48} +(0.415990 + 1.55250i) q^{50} +(-3.30589 - 1.90866i) q^{51} +(0.177238 - 2.91241i) q^{52} +(-3.16223 - 5.47715i) q^{53} +(-5.77504 - 1.54742i) q^{54} +(1.70918 + 0.986797i) q^{55} +(1.26614 + 1.26614i) q^{57} +(8.66852 + 8.66852i) q^{58} +(-0.491481 + 0.131692i) q^{59} +(1.00213 + 0.268520i) q^{60} -13.0284i q^{61} +(7.24196 - 12.5434i) q^{62} -2.67342i q^{64} +(-5.42698 + 4.80434i) q^{65} +(-0.908836 + 0.524717i) q^{66} +(0.606011 + 0.606011i) q^{67} +(4.19491 - 2.42193i) q^{68} +(-0.953100 - 1.65082i) q^{69} +(-3.01121 + 11.2380i) q^{71} +(-3.65973 + 3.65973i) q^{72} +(0.377014 - 1.40704i) q^{73} +(-4.01968 + 6.96230i) q^{74} +(0.305782 + 0.529629i) q^{75} +(-2.19469 + 0.588064i) q^{76} +(-0.769526 - 3.77644i) q^{78} +(5.80137 - 10.0483i) q^{79} +(7.05555 - 7.05555i) q^{80} +5.50492 q^{81} -5.73802 q^{82} +(1.23779 - 1.23779i) q^{83} +(-11.6225 - 3.11424i) q^{85} +(-0.374999 - 1.39951i) q^{86} +(4.03966 + 2.33230i) q^{87} +1.95941i q^{88} +(-2.07729 + 7.75255i) q^{89} -8.73759 q^{90} +2.41881 q^{92} +(1.42638 - 5.32334i) q^{93} -5.14367i q^{94} +(4.88792 + 2.82204i) q^{95} +(0.714359 + 2.66602i) q^{96} +(12.0756 + 3.23566i) q^{97} +(1.80030 - 1.80030i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 32q + 4q^{2} + 12q^{4} - 16q^{8} - 16q^{9} + O(q^{10}) \) \( 32q + 4q^{2} + 12q^{4} - 16q^{8} - 16q^{9} + 20q^{11} - 8q^{15} + 12q^{16} - 64q^{18} + 4q^{22} + 12q^{23} + 4q^{29} + 64q^{32} + 4q^{37} + 36q^{39} - 48q^{43} - 84q^{44} - 108q^{46} - 44q^{50} + 12q^{51} - 36q^{53} - 92q^{57} + 44q^{58} + 28q^{60} + 28q^{65} + 64q^{67} + 84q^{71} + 4q^{72} - 24q^{74} + 148q^{78} + 40q^{79} - 56q^{81} + 36q^{85} + 108q^{86} + 24q^{92} - 24q^{93} + 84q^{95} - 60q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/637\mathbb{Z}\right)^\times\).

\(n\) \(197\) \(248\)
\(\chi(n)\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{5}{6}\right)\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.433802 + 1.61897i −0.306744 + 1.14479i 0.624689 + 0.780873i \(0.285226\pi\)
−0.931433 + 0.363912i \(0.881441\pi\)
\(3\) 0.637748i 0.368204i 0.982907 + 0.184102i \(0.0589377\pi\)
−0.982907 + 0.184102i \(0.941062\pi\)
\(4\) −0.700831 0.404625i −0.350416 0.202313i
\(5\) 0.520288 + 1.94174i 0.232680 + 0.868373i 0.979181 + 0.202989i \(0.0650656\pi\)
−0.746501 + 0.665384i \(0.768268\pi\)
\(6\) −1.03250 0.276656i −0.421515 0.112945i
\(7\) 0 0
\(8\) −1.41124 + 1.41124i −0.498948 + 0.498948i
\(9\) 2.59328 0.864426
\(10\) −3.36932 −1.06547
\(11\) 0.694217 0.694217i 0.209314 0.209314i −0.594662 0.803976i \(-0.702714\pi\)
0.803976 + 0.594662i \(0.202714\pi\)
\(12\) 0.258049 0.446954i 0.0744924 0.129025i
\(13\) 1.60977 + 3.22624i 0.446471 + 0.894798i
\(14\) 0 0
\(15\) −1.23834 + 0.331813i −0.319739 + 0.0856737i
\(16\) −2.48181 4.29862i −0.620452 1.07465i
\(17\) −2.99281 + 5.18370i −0.725863 + 1.25723i 0.232755 + 0.972535i \(0.425226\pi\)
−0.958618 + 0.284696i \(0.908107\pi\)
\(18\) −1.12497 + 4.19844i −0.265158 + 0.989582i
\(19\) 1.98532 1.98532i 0.455464 0.455464i −0.441699 0.897163i \(-0.645624\pi\)
0.897163 + 0.441699i \(0.145624\pi\)
\(20\) 0.421043 1.57135i 0.0941481 0.351366i
\(21\) 0 0
\(22\) 0.822765 + 1.42507i 0.175414 + 0.303826i
\(23\) −2.58851 + 1.49448i −0.539742 + 0.311620i −0.744974 0.667093i \(-0.767538\pi\)
0.205233 + 0.978713i \(0.434205\pi\)
\(24\) −0.900016 0.900016i −0.183715 0.183715i
\(25\) 0.830467 0.479471i 0.166093 0.0958941i
\(26\) −5.92151 + 1.20663i −1.16130 + 0.236639i
\(27\) 3.56710i 0.686489i
\(28\) 0 0
\(29\) 3.65708 6.33425i 0.679103 1.17624i −0.296148 0.955142i \(-0.595702\pi\)
0.975251 0.221099i \(-0.0709645\pi\)
\(30\) 2.14878i 0.392312i
\(31\) −8.34708 2.23659i −1.49918 0.401704i −0.586354 0.810055i \(-0.699437\pi\)
−0.912825 + 0.408351i \(0.866104\pi\)
\(32\) 4.18037 1.12013i 0.738992 0.198012i
\(33\) 0.442736 + 0.442736i 0.0770704 + 0.0770704i
\(34\) −7.09397 7.09397i −1.21661 1.21661i
\(35\) 0 0
\(36\) −1.81745 1.04931i −0.302908 0.174884i
\(37\) 4.63309 + 1.24143i 0.761675 + 0.204090i 0.618690 0.785635i \(-0.287664\pi\)
0.142984 + 0.989725i \(0.454330\pi\)
\(38\) 2.35294 + 4.07541i 0.381697 + 0.661119i
\(39\) −2.05753 + 1.02663i −0.329468 + 0.164393i
\(40\) −3.47451 2.00601i −0.549369 0.317178i
\(41\) 0.886060 + 3.30682i 0.138379 + 0.516439i 0.999961 + 0.00881984i \(0.00280748\pi\)
−0.861582 + 0.507619i \(0.830526\pi\)
\(42\) 0 0
\(43\) −0.748633 + 0.432224i −0.114165 + 0.0659135i −0.555995 0.831185i \(-0.687663\pi\)
0.441830 + 0.897099i \(0.354329\pi\)
\(44\) −0.767427 + 0.205631i −0.115694 + 0.0310001i
\(45\) 1.34925 + 5.03547i 0.201134 + 0.750644i
\(46\) −1.29661 4.83903i −0.191175 0.713476i
\(47\) −2.96429 + 0.794280i −0.432387 + 0.115858i −0.468446 0.883492i \(-0.655186\pi\)
0.0360596 + 0.999350i \(0.488519\pi\)
\(48\) 2.74144 1.58277i 0.395692 0.228453i
\(49\) 0 0
\(50\) 0.415990 + 1.55250i 0.0588299 + 0.219556i
\(51\) −3.30589 1.90866i −0.462918 0.267266i
\(52\) 0.177238 2.91241i 0.0245784 0.403878i
\(53\) −3.16223 5.47715i −0.434366 0.752344i 0.562878 0.826540i \(-0.309694\pi\)
−0.997244 + 0.0741963i \(0.976361\pi\)
\(54\) −5.77504 1.54742i −0.785883 0.210577i
\(55\) 1.70918 + 0.986797i 0.230466 + 0.133060i
\(56\) 0 0
\(57\) 1.26614 + 1.26614i 0.167704 + 0.167704i
\(58\) 8.66852 + 8.66852i 1.13823 + 1.13823i
\(59\) −0.491481 + 0.131692i −0.0639854 + 0.0171448i −0.290670 0.956823i \(-0.593878\pi\)
0.226684 + 0.973968i \(0.427211\pi\)
\(60\) 1.00213 + 0.268520i 0.129374 + 0.0346657i
\(61\) 13.0284i 1.66811i −0.551679 0.834057i \(-0.686012\pi\)
0.551679 0.834057i \(-0.313988\pi\)
\(62\) 7.24196 12.5434i 0.919729 1.59302i
\(63\) 0 0
\(64\) 2.67342i 0.334178i
\(65\) −5.42698 + 4.80434i −0.673134 + 0.595905i
\(66\) −0.908836 + 0.524717i −0.111870 + 0.0645882i
\(67\) 0.606011 + 0.606011i 0.0740361 + 0.0740361i 0.743155 0.669119i \(-0.233328\pi\)
−0.669119 + 0.743155i \(0.733328\pi\)
\(68\) 4.19491 2.42193i 0.508707 0.293702i
\(69\) −0.953100 1.65082i −0.114740 0.198735i
\(70\) 0 0
\(71\) −3.01121 + 11.2380i −0.357365 + 1.33370i 0.520117 + 0.854095i \(0.325888\pi\)
−0.877482 + 0.479609i \(0.840778\pi\)
\(72\) −3.65973 + 3.65973i −0.431304 + 0.431304i
\(73\) 0.377014 1.40704i 0.0441262 0.164681i −0.940347 0.340217i \(-0.889499\pi\)
0.984473 + 0.175536i \(0.0561660\pi\)
\(74\) −4.01968 + 6.96230i −0.467279 + 0.809350i
\(75\) 0.305782 + 0.529629i 0.0353086 + 0.0611563i
\(76\) −2.19469 + 0.588064i −0.251748 + 0.0674556i
\(77\) 0 0
\(78\) −0.769526 3.77644i −0.0871316 0.427597i
\(79\) 5.80137 10.0483i 0.652705 1.13052i −0.329758 0.944065i \(-0.606967\pi\)
0.982464 0.186454i \(-0.0596994\pi\)
\(80\) 7.05555 7.05555i 0.788834 0.788834i
\(81\) 5.50492 0.611657
\(82\) −5.73802 −0.633658
\(83\) 1.23779 1.23779i 0.135865 0.135865i −0.635904 0.771768i \(-0.719372\pi\)
0.771768 + 0.635904i \(0.219372\pi\)
\(84\) 0 0
\(85\) −11.6225 3.11424i −1.26064 0.337787i
\(86\) −0.374999 1.39951i −0.0404372 0.150914i
\(87\) 4.03966 + 2.33230i 0.433097 + 0.250049i
\(88\) 1.95941i 0.208874i
\(89\) −2.07729 + 7.75255i −0.220192 + 0.821769i 0.764082 + 0.645120i \(0.223193\pi\)
−0.984274 + 0.176649i \(0.943474\pi\)
\(90\) −8.73759 −0.921023
\(91\) 0 0
\(92\) 2.41881 0.252179
\(93\) 1.42638 5.32334i 0.147909 0.552004i
\(94\) 5.14367i 0.530529i
\(95\) 4.88792 + 2.82204i 0.501490 + 0.289535i
\(96\) 0.714359 + 2.66602i 0.0729090 + 0.272100i
\(97\) 12.0756 + 3.23566i 1.22609 + 0.328531i 0.813058 0.582183i \(-0.197801\pi\)
0.413037 + 0.910714i \(0.364468\pi\)
\(98\) 0 0
\(99\) 1.80030 1.80030i 0.180937 0.180937i
\(100\) −0.776023 −0.0776023
\(101\) 7.99635 0.795667 0.397833 0.917458i \(-0.369762\pi\)
0.397833 + 0.917458i \(0.369762\pi\)
\(102\) 4.52417 4.52417i 0.447959 0.447959i
\(103\) 5.16928 8.95345i 0.509344 0.882210i −0.490597 0.871386i \(-0.663221\pi\)
0.999941 0.0108235i \(-0.00344528\pi\)
\(104\) −6.82477 2.28122i −0.669224 0.223692i
\(105\) 0 0
\(106\) 10.2391 2.74356i 0.994511 0.266479i
\(107\) −6.52593 11.3032i −0.630885 1.09273i −0.987371 0.158425i \(-0.949358\pi\)
0.356486 0.934301i \(-0.383975\pi\)
\(108\) 1.44334 2.49994i 0.138885 0.240557i
\(109\) −3.03074 + 11.3109i −0.290292 + 1.08339i 0.654592 + 0.755982i \(0.272840\pi\)
−0.944885 + 0.327403i \(0.893826\pi\)
\(110\) −2.33904 + 2.33904i −0.223019 + 0.223019i
\(111\) −0.791721 + 2.95474i −0.0751468 + 0.280452i
\(112\) 0 0
\(113\) 4.05748 + 7.02777i 0.381696 + 0.661117i 0.991305 0.131586i \(-0.0420069\pi\)
−0.609609 + 0.792702i \(0.708674\pi\)
\(114\) −2.59909 + 1.50058i −0.243427 + 0.140543i
\(115\) −4.24866 4.24866i −0.396189 0.396189i
\(116\) −5.12600 + 2.95950i −0.475937 + 0.274782i
\(117\) 4.17459 + 8.36653i 0.385941 + 0.773486i
\(118\) 0.852822i 0.0785086i
\(119\) 0 0
\(120\) 1.27933 2.21587i 0.116786 0.202280i
\(121\) 10.0361i 0.912375i
\(122\) 21.0926 + 5.65174i 1.90963 + 0.511684i
\(123\) −2.10892 + 0.565083i −0.190155 + 0.0509518i
\(124\) 4.94491 + 4.94491i 0.444066 + 0.444066i
\(125\) 8.47036 + 8.47036i 0.757612 + 0.757612i
\(126\) 0 0
\(127\) 6.81853 + 3.93668i 0.605047 + 0.349324i 0.771024 0.636805i \(-0.219745\pi\)
−0.165977 + 0.986130i \(0.553078\pi\)
\(128\) 12.6889 + 3.39999i 1.12155 + 0.300519i
\(129\) −0.275650 0.477440i −0.0242696 0.0420362i
\(130\) −5.42385 10.8702i −0.475703 0.953384i
\(131\) 17.2856 + 9.97987i 1.51025 + 0.871945i 0.999928 + 0.0119634i \(0.00380815\pi\)
0.510325 + 0.859982i \(0.329525\pi\)
\(132\) −0.131141 0.489425i −0.0114144 0.0425990i
\(133\) 0 0
\(134\) −1.24400 + 0.718226i −0.107466 + 0.0620452i
\(135\) −6.92639 + 1.85592i −0.596129 + 0.159732i
\(136\) −3.09187 11.5390i −0.265125 0.989461i
\(137\) −2.78324 10.3872i −0.237788 0.887437i −0.976872 0.213824i \(-0.931408\pi\)
0.739084 0.673613i \(-0.235259\pi\)
\(138\) 3.08608 0.826913i 0.262705 0.0703915i
\(139\) −14.1096 + 8.14616i −1.19676 + 0.690949i −0.959831 0.280579i \(-0.909474\pi\)
−0.236927 + 0.971527i \(0.576140\pi\)
\(140\) 0 0
\(141\) −0.506551 1.89047i −0.0426593 0.159207i
\(142\) −16.8877 9.75012i −1.41719 0.818212i
\(143\) 3.35724 + 1.12218i 0.280747 + 0.0938413i
\(144\) −6.43601 11.1475i −0.536334 0.928959i
\(145\) 14.2022 + 3.80547i 1.17943 + 0.316027i
\(146\) 2.11440 + 1.22075i 0.174989 + 0.101030i
\(147\) 0 0
\(148\) −2.74470 2.74470i −0.225613 0.225613i
\(149\) 13.2274 + 13.2274i 1.08363 + 1.08363i 0.996168 + 0.0874634i \(0.0278761\pi\)
0.0874634 + 0.996168i \(0.472124\pi\)
\(150\) −0.990103 + 0.265297i −0.0808416 + 0.0216614i
\(151\) 0.0351934 + 0.00943004i 0.00286400 + 0.000767406i 0.260251 0.965541i \(-0.416195\pi\)
−0.257387 + 0.966308i \(0.582861\pi\)
\(152\) 5.60353i 0.454506i
\(153\) −7.76118 + 13.4428i −0.627454 + 1.08678i
\(154\) 0 0
\(155\) 17.3715i 1.39532i
\(156\) 1.85738 + 0.113033i 0.148710 + 0.00904988i
\(157\) −6.22554 + 3.59432i −0.496852 + 0.286858i −0.727413 0.686200i \(-0.759277\pi\)
0.230560 + 0.973058i \(0.425944\pi\)
\(158\) 13.7512 + 13.7512i 1.09399 + 1.09399i
\(159\) 3.49304 2.01671i 0.277016 0.159935i
\(160\) 4.34999 + 7.53441i 0.343897 + 0.595647i
\(161\) 0 0
\(162\) −2.38804 + 8.91230i −0.187622 + 0.700216i
\(163\) −11.6359 + 11.6359i −0.911397 + 0.911397i −0.996382 0.0849855i \(-0.972916\pi\)
0.0849855 + 0.996382i \(0.472916\pi\)
\(164\) 0.717044 2.67605i 0.0559918 0.208964i
\(165\) −0.629328 + 1.09003i −0.0489932 + 0.0848586i
\(166\) 1.46699 + 2.54090i 0.113860 + 0.197212i
\(167\) 6.49344 1.73991i 0.502478 0.134638i 0.00132801 0.999999i \(-0.499577\pi\)
0.501150 + 0.865361i \(0.332911\pi\)
\(168\) 0 0
\(169\) −7.81725 + 10.3870i −0.601327 + 0.799003i
\(170\) 10.0837 17.4656i 0.773388 1.33955i
\(171\) 5.14849 5.14849i 0.393715 0.393715i
\(172\) 0.699554 0.0533405
\(173\) 9.51731 0.723587 0.361794 0.932258i \(-0.382164\pi\)
0.361794 + 0.932258i \(0.382164\pi\)
\(174\) −5.52834 + 5.52834i −0.419102 + 0.419102i
\(175\) 0 0
\(176\) −4.70709 1.26126i −0.354810 0.0950711i
\(177\) −0.0839864 0.313441i −0.00631280 0.0235597i
\(178\) −11.6500 6.72614i −0.873206 0.504146i
\(179\) 6.00707i 0.448989i 0.974475 + 0.224495i \(0.0720731\pi\)
−0.974475 + 0.224495i \(0.927927\pi\)
\(180\) 1.09188 4.07496i 0.0813841 0.303729i
\(181\) 6.05960 0.450407 0.225203 0.974312i \(-0.427695\pi\)
0.225203 + 0.974312i \(0.427695\pi\)
\(182\) 0 0
\(183\) 8.30883 0.614207
\(184\) 1.54394 5.76207i 0.113821 0.424786i
\(185\) 9.64216i 0.708905i
\(186\) 7.99956 + 4.61855i 0.586556 + 0.338648i
\(187\) 1.52095 + 5.67627i 0.111223 + 0.415090i
\(188\) 2.39886 + 0.642771i 0.174955 + 0.0468789i
\(189\) 0 0
\(190\) −6.68919 + 6.68919i −0.485285 + 0.485285i
\(191\) 21.6273 1.56490 0.782449 0.622715i \(-0.213970\pi\)
0.782449 + 0.622715i \(0.213970\pi\)
\(192\) 1.70497 0.123046
\(193\) 6.85258 6.85258i 0.493260 0.493260i −0.416072 0.909332i \(-0.636594\pi\)
0.909332 + 0.416072i \(0.136594\pi\)
\(194\) −10.4769 + 18.1465i −0.752195 + 1.30284i
\(195\) −3.06396 3.46105i −0.219415 0.247851i
\(196\) 0 0
\(197\) −4.47322 + 1.19859i −0.318704 + 0.0853964i −0.414624 0.909993i \(-0.636087\pi\)
0.0959210 + 0.995389i \(0.469420\pi\)
\(198\) 2.13366 + 3.69560i 0.151632 + 0.262635i
\(199\) 10.7801 18.6717i 0.764182 1.32360i −0.176496 0.984301i \(-0.556476\pi\)
0.940678 0.339300i \(-0.110190\pi\)
\(200\) −0.495341 + 1.84864i −0.0350259 + 0.130718i
\(201\) −0.386483 + 0.386483i −0.0272604 + 0.0272604i
\(202\) −3.46883 + 12.9459i −0.244066 + 0.910868i
\(203\) 0 0
\(204\) 1.54458 + 2.67530i 0.108142 + 0.187308i
\(205\) −5.95998 + 3.44100i −0.416263 + 0.240330i
\(206\) 12.2529 + 12.2529i 0.853702 + 0.853702i
\(207\) −6.71272 + 3.87559i −0.466566 + 0.269372i
\(208\) 9.87322 14.9267i 0.684585 1.03498i
\(209\) 2.75649i 0.190670i
\(210\) 0 0
\(211\) 7.39505 12.8086i 0.509096 0.881780i −0.490848 0.871245i \(-0.663313\pi\)
0.999945 0.0105352i \(-0.00335353\pi\)
\(212\) 5.11807i 0.351511i
\(213\) −7.16701 1.92039i −0.491076 0.131583i
\(214\) 21.1306 5.66192i 1.44446 0.387041i
\(215\) −1.22877 1.22877i −0.0838015 0.0838015i
\(216\) −5.03404 5.03404i −0.342523 0.342523i
\(217\) 0 0
\(218\) −16.9972 9.81336i −1.15120 0.664644i
\(219\) 0.897335 + 0.240440i 0.0606363 + 0.0162474i
\(220\) −0.798566 1.38316i −0.0538393 0.0932524i
\(221\) −21.5416 1.31094i −1.44904 0.0881832i
\(222\) −4.44019 2.56355i −0.298006 0.172054i
\(223\) −5.52568 20.6221i −0.370027 1.38096i −0.860477 0.509490i \(-0.829834\pi\)
0.490450 0.871469i \(-0.336832\pi\)
\(224\) 0 0
\(225\) 2.15363 1.24340i 0.143575 0.0828933i
\(226\) −13.1379 + 3.52029i −0.873919 + 0.234166i
\(227\) 3.49849 + 13.0566i 0.232203 + 0.866594i 0.979390 + 0.201980i \(0.0647375\pi\)
−0.747186 + 0.664615i \(0.768596\pi\)
\(228\) −0.375037 1.39966i −0.0248374 0.0926946i
\(229\) −6.94692 + 1.86142i −0.459066 + 0.123006i −0.480938 0.876755i \(-0.659704\pi\)
0.0218726 + 0.999761i \(0.493037\pi\)
\(230\) 8.72153 5.03538i 0.575081 0.332023i
\(231\) 0 0
\(232\) 3.77813 + 14.1002i 0.248046 + 0.925721i
\(233\) −20.0959 11.6024i −1.31653 0.760097i −0.333359 0.942800i \(-0.608182\pi\)
−0.983168 + 0.182702i \(0.941515\pi\)
\(234\) −15.3561 + 3.12912i −1.00386 + 0.204557i
\(235\) −3.08457 5.34264i −0.201215 0.348515i
\(236\) 0.397731 + 0.106572i 0.0258901 + 0.00693723i
\(237\) 6.40827 + 3.69982i 0.416262 + 0.240329i
\(238\) 0 0
\(239\) −2.77302 2.77302i −0.179372 0.179372i 0.611710 0.791082i \(-0.290482\pi\)
−0.791082 + 0.611710i \(0.790482\pi\)
\(240\) 4.49966 + 4.49966i 0.290452 + 0.290452i
\(241\) 3.08037 0.825382i 0.198424 0.0531675i −0.158238 0.987401i \(-0.550581\pi\)
0.356662 + 0.934233i \(0.383915\pi\)
\(242\) −16.2482 4.35369i −1.04447 0.279866i
\(243\) 14.2121i 0.911704i
\(244\) −5.27161 + 9.13070i −0.337480 + 0.584533i
\(245\) 0 0
\(246\) 3.65941i 0.233316i
\(247\) 9.60104 + 3.20920i 0.610900 + 0.204197i
\(248\) 14.9361 8.62336i 0.948443 0.547584i
\(249\) 0.789397 + 0.789397i 0.0500260 + 0.0500260i
\(250\) −17.3877 + 10.0388i −1.09970 + 0.634910i
\(251\) −5.89697 10.2138i −0.372213 0.644692i 0.617692 0.786420i \(-0.288068\pi\)
−0.989906 + 0.141727i \(0.954734\pi\)
\(252\) 0 0
\(253\) −0.759496 + 2.83448i −0.0477491 + 0.178202i
\(254\) −9.33127 + 9.33127i −0.585496 + 0.585496i
\(255\) 1.98610 7.41224i 0.124375 0.464173i
\(256\) −8.33554 + 14.4376i −0.520971 + 0.902349i
\(257\) −8.34519 14.4543i −0.520559 0.901634i −0.999714 0.0239041i \(-0.992390\pi\)
0.479156 0.877730i \(-0.340943\pi\)
\(258\) 0.892538 0.239155i 0.0555670 0.0148891i
\(259\) 0 0
\(260\) 5.74735 1.17114i 0.356436 0.0726310i
\(261\) 9.48383 16.4265i 0.587034 1.01677i
\(262\) −23.6557 + 23.6557i −1.46145 + 1.46145i
\(263\) 9.51537 0.586743 0.293371 0.955999i \(-0.405223\pi\)
0.293371 + 0.955999i \(0.405223\pi\)
\(264\) −1.24961 −0.0769083
\(265\) 8.98993 8.98993i 0.552247 0.552247i
\(266\) 0 0
\(267\) −4.94418 1.32479i −0.302579 0.0810758i
\(268\) −0.179504 0.669919i −0.0109650 0.0409218i
\(269\) 0.275945 + 0.159317i 0.0168247 + 0.00971373i 0.508389 0.861128i \(-0.330241\pi\)
−0.491564 + 0.870841i \(0.663575\pi\)
\(270\) 12.0187i 0.731437i
\(271\) 6.94654 25.9248i 0.421972 1.57482i −0.348475 0.937318i \(-0.613300\pi\)
0.770447 0.637504i \(-0.220033\pi\)
\(272\) 29.7103 1.80145
\(273\) 0 0
\(274\) 18.0239 1.08886
\(275\) 0.243668 0.909381i 0.0146937 0.0548378i
\(276\) 1.54259i 0.0928532i
\(277\) 13.1218 + 7.57587i 0.788412 + 0.455190i 0.839403 0.543509i \(-0.182905\pi\)
−0.0509909 + 0.998699i \(0.516238\pi\)
\(278\) −7.06764 26.3768i −0.423889 1.58198i
\(279\) −21.6463 5.80010i −1.29593 0.347243i
\(280\) 0 0
\(281\) 5.40600 5.40600i 0.322495 0.322495i −0.527228 0.849724i \(-0.676769\pi\)
0.849724 + 0.527228i \(0.176769\pi\)
\(282\) 3.28036 0.195343
\(283\) −1.79244 −0.106549 −0.0532746 0.998580i \(-0.516966\pi\)
−0.0532746 + 0.998580i \(0.516966\pi\)
\(284\) 6.65752 6.65752i 0.395051 0.395051i
\(285\) −1.79975 + 3.11726i −0.106608 + 0.184651i
\(286\) −3.27315 + 4.94848i −0.193546 + 0.292610i
\(287\) 0 0
\(288\) 10.8409 2.90480i 0.638803 0.171167i
\(289\) −9.41380 16.3052i −0.553753 0.959128i
\(290\) −12.3219 + 21.3422i −0.723567 + 1.25325i
\(291\) −2.06353 + 7.70122i −0.120967 + 0.451453i
\(292\) −0.833545 + 0.833545i −0.0487796 + 0.0487796i
\(293\) 6.85691 25.5903i 0.400585 1.49500i −0.411471 0.911423i \(-0.634985\pi\)
0.812055 0.583580i \(-0.198349\pi\)
\(294\) 0 0
\(295\) −0.511424 0.885812i −0.0297762 0.0515739i
\(296\) −8.29035 + 4.78644i −0.481867 + 0.278206i
\(297\) 2.47634 + 2.47634i 0.143692 + 0.143692i
\(298\) −27.1529 + 15.6767i −1.57292 + 0.908127i
\(299\) −8.98846 5.94538i −0.519816 0.343830i
\(300\) 0.494908i 0.0285735i
\(301\) 0 0
\(302\) −0.0305339 + 0.0528863i −0.00175703 + 0.00304327i
\(303\) 5.09966i 0.292968i
\(304\) −13.4613 3.60695i −0.772059 0.206873i
\(305\) 25.2978 6.77851i 1.44855 0.388136i
\(306\) −18.3966 18.3966i −1.05166 1.05166i
\(307\) −1.54710 1.54710i −0.0882978 0.0882978i 0.661578 0.749876i \(-0.269887\pi\)
−0.749876 + 0.661578i \(0.769887\pi\)
\(308\) 0 0
\(309\) 5.71005 + 3.29670i 0.324833 + 0.187543i
\(310\) 28.1240 + 7.53581i 1.59734 + 0.428005i
\(311\) −14.6672 25.4043i −0.831699 1.44055i −0.896690 0.442660i \(-0.854035\pi\)
0.0649904 0.997886i \(-0.479298\pi\)
\(312\) 1.45484 4.35249i 0.0823644 0.246411i
\(313\) −24.2354 13.9923i −1.36987 0.790893i −0.378957 0.925414i \(-0.623717\pi\)
−0.990911 + 0.134521i \(0.957050\pi\)
\(314\) −3.11844 11.6382i −0.175984 0.656781i
\(315\) 0 0
\(316\) −8.13157 + 4.69476i −0.457436 + 0.264101i
\(317\) −7.59654 + 2.03549i −0.426664 + 0.114324i −0.465760 0.884911i \(-0.654219\pi\)
0.0390957 + 0.999235i \(0.487552\pi\)
\(318\) 1.74970 + 6.52998i 0.0981185 + 0.366183i
\(319\) −1.85854 6.93616i −0.104058 0.388350i
\(320\) 5.19109 1.39095i 0.290191 0.0777564i
\(321\) 7.20862 4.16190i 0.402346 0.232295i
\(322\) 0 0
\(323\) 4.34961 + 16.2330i 0.242019 + 0.903227i
\(324\) −3.85802 2.22743i −0.214334 0.123746i
\(325\) 2.88375 + 1.90745i 0.159962 + 0.105806i
\(326\) −13.7905 23.8859i −0.763788 1.32292i
\(327\) −7.21349 1.93285i −0.398907 0.106887i
\(328\) −5.91716 3.41627i −0.326720 0.188632i
\(329\) 0 0
\(330\) −1.49172 1.49172i −0.0821165 0.0821165i
\(331\) 11.5133 + 11.5133i 0.632826 + 0.632826i 0.948776 0.315950i \(-0.102323\pi\)
−0.315950 + 0.948776i \(0.602323\pi\)
\(332\) −1.36832 + 0.366640i −0.0750963 + 0.0201220i
\(333\) 12.0149 + 3.21938i 0.658411 + 0.176421i
\(334\) 11.2675i 0.616529i
\(335\) −0.861417 + 1.49202i −0.0470642 + 0.0815176i
\(336\) 0 0
\(337\) 11.0114i 0.599827i −0.953966 0.299913i \(-0.903042\pi\)
0.953966 0.299913i \(-0.0969578\pi\)
\(338\) −13.4252 17.1618i −0.730233 0.933480i
\(339\) −4.48195 + 2.58765i −0.243426 + 0.140542i
\(340\) 6.88532 + 6.88532i 0.373409 + 0.373409i
\(341\) −7.34737 + 4.24200i −0.397882 + 0.229717i
\(342\) 6.10183 + 10.5687i 0.329949 + 0.571488i
\(343\) 0 0
\(344\) 0.446530 1.66647i 0.0240753 0.0898501i
\(345\) 2.70957 2.70957i 0.145879 0.145879i
\(346\) −4.12863 + 15.4082i −0.221956 + 0.828352i
\(347\) −2.36362 + 4.09391i −0.126886 + 0.219772i −0.922468 0.386073i \(-0.873831\pi\)
0.795583 + 0.605845i \(0.207165\pi\)
\(348\) −1.88741 3.26910i −0.101176 0.175242i
\(349\) −22.4353 + 6.01151i −1.20093 + 0.321789i −0.803198 0.595712i \(-0.796870\pi\)
−0.397734 + 0.917501i \(0.630203\pi\)
\(350\) 0 0
\(351\) −11.5083 + 5.74223i −0.614269 + 0.306498i
\(352\) 2.12447 3.67970i 0.113235 0.196128i
\(353\) −9.29908 + 9.29908i −0.494940 + 0.494940i −0.909859 0.414919i \(-0.863810\pi\)
0.414919 + 0.909859i \(0.363810\pi\)
\(354\) 0.543886 0.0289072
\(355\) −23.3880 −1.24130
\(356\) 4.59271 4.59271i 0.243413 0.243413i
\(357\) 0 0
\(358\) −9.72526 2.60588i −0.513996 0.137725i
\(359\) 2.43301 + 9.08010i 0.128409 + 0.479229i 0.999938 0.0111144i \(-0.00353790\pi\)
−0.871529 + 0.490344i \(0.836871\pi\)
\(360\) −9.01037 5.20214i −0.474888 0.274177i
\(361\) 11.1170i 0.585105i
\(362\) −2.62867 + 9.81032i −0.138160 + 0.515619i
\(363\) −6.40052 −0.335940
\(364\) 0 0
\(365\) 2.92826 0.153272
\(366\) −3.60439 + 13.4518i −0.188404 + 0.703135i
\(367\) 7.31961i 0.382081i 0.981582 + 0.191040i \(0.0611861\pi\)
−0.981582 + 0.191040i \(0.938814\pi\)
\(368\) 12.8484 + 7.41801i 0.669767 + 0.386690i
\(369\) 2.29780 + 8.57550i 0.119619 + 0.446423i
\(370\) −15.6104 4.18279i −0.811544 0.217453i
\(371\) 0 0
\(372\) −3.15361 + 3.15361i −0.163507 + 0.163507i
\(373\) −1.08512 −0.0561856 −0.0280928 0.999605i \(-0.508943\pi\)
−0.0280928 + 0.999605i \(0.508943\pi\)
\(374\) −9.84951 −0.509306
\(375\) −5.40196 + 5.40196i −0.278956 + 0.278956i
\(376\) 3.06241 5.30425i 0.157932 0.273546i
\(377\) 26.3229 + 1.60191i 1.35570 + 0.0825025i
\(378\) 0 0
\(379\) −25.1695 + 6.74414i −1.29287 + 0.346423i −0.838749 0.544518i \(-0.816713\pi\)
−0.454119 + 0.890941i \(0.650046\pi\)
\(380\) −2.28374 3.95555i −0.117153 0.202915i
\(381\) −2.51061 + 4.34851i −0.128623 + 0.222781i
\(382\) −9.38197 + 35.0140i −0.480023 + 1.79147i
\(383\) 3.76918 3.76918i 0.192596 0.192596i −0.604221 0.796817i \(-0.706516\pi\)
0.796817 + 0.604221i \(0.206516\pi\)
\(384\) −2.16834 + 8.09234i −0.110652 + 0.412961i
\(385\) 0 0
\(386\) 8.12146 + 14.0668i 0.413372 + 0.715981i
\(387\) −1.94141 + 1.12088i −0.0986876 + 0.0569773i
\(388\) −7.15375 7.15375i −0.363177 0.363177i
\(389\) −2.97841 + 1.71958i −0.151011 + 0.0871864i −0.573602 0.819134i \(-0.694454\pi\)
0.422590 + 0.906321i \(0.361121\pi\)
\(390\) 6.93249 3.45905i 0.351040 0.175156i
\(391\) 17.8907i 0.904773i
\(392\) 0 0
\(393\) −6.36465 + 11.0239i −0.321054 + 0.556082i
\(394\) 7.76196i 0.391042i
\(395\) 22.5295 + 6.03677i 1.13358 + 0.303743i
\(396\) −1.99015 + 0.533259i −0.100009 + 0.0267973i
\(397\) 0.424872 + 0.424872i 0.0213237 + 0.0213237i 0.717688 0.696365i \(-0.245200\pi\)
−0.696365 + 0.717688i \(0.745200\pi\)
\(398\) 25.5525 + 25.5525i 1.28083 + 1.28083i
\(399\) 0 0
\(400\) −4.12212 2.37991i −0.206106 0.118995i
\(401\) −11.5834 3.10377i −0.578448 0.154995i −0.0422800 0.999106i \(-0.513462\pi\)
−0.536168 + 0.844111i \(0.680129\pi\)
\(402\) −0.458047 0.793361i −0.0228453 0.0395693i
\(403\) −6.22113 30.5301i −0.309896 1.52081i
\(404\) −5.60409 3.23553i −0.278814 0.160973i
\(405\) 2.86414 + 10.6891i 0.142320 + 0.531147i
\(406\) 0 0
\(407\) 4.07819 2.35454i 0.202148 0.116710i
\(408\) 7.35898 1.97183i 0.364324 0.0976203i
\(409\) −3.00424 11.2120i −0.148550 0.554396i −0.999572 0.0292657i \(-0.990683\pi\)
0.851022 0.525131i \(-0.175984\pi\)
\(410\) −2.98542 11.1418i −0.147440 0.550252i
\(411\) 6.62441 1.77501i 0.326758 0.0875546i
\(412\) −7.24558 + 4.18324i −0.356964 + 0.206093i
\(413\) 0 0
\(414\) −3.36248 12.5489i −0.165257 0.616747i
\(415\) 3.04747 + 1.75946i 0.149594 + 0.0863683i
\(416\) 10.3432 + 11.6837i 0.507119 + 0.572842i
\(417\) −5.19520 8.99836i −0.254410 0.440651i
\(418\) 4.46267 + 1.19577i 0.218276 + 0.0584870i
\(419\) −30.9881 17.8910i −1.51387 0.874032i −0.999868 0.0162408i \(-0.994830\pi\)
−0.513999 0.857791i \(-0.671836\pi\)
\(420\) 0 0
\(421\) −3.47255 3.47255i −0.169242 0.169242i 0.617404 0.786646i \(-0.288184\pi\)
−0.786646 + 0.617404i \(0.788184\pi\)
\(422\) 17.5288 + 17.5288i 0.853287 + 0.853287i
\(423\) −7.68723 + 2.05979i −0.373766 + 0.100150i
\(424\) 12.1922 + 3.26690i 0.592107 + 0.158655i
\(425\) 5.73985i 0.278424i
\(426\) 6.21813 10.7701i 0.301269 0.521814i
\(427\) 0 0
\(428\) 10.5622i 0.510544i
\(429\) −0.715668 + 2.14108i −0.0345528 + 0.103372i
\(430\) 2.52239 1.45630i 0.121640 0.0702291i
\(431\) 0.347144 + 0.347144i 0.0167213 + 0.0167213i 0.715418 0.698697i \(-0.246236\pi\)
−0.698697 + 0.715418i \(0.746236\pi\)
\(432\) 15.3336 8.85286i 0.737739 0.425934i
\(433\) 8.89347 + 15.4039i 0.427393 + 0.740266i 0.996641 0.0818999i \(-0.0260988\pi\)
−0.569248 + 0.822166i \(0.692765\pi\)
\(434\) 0 0
\(435\) −2.42693 + 9.05744i −0.116363 + 0.434271i
\(436\) 6.70070 6.70070i 0.320905 0.320905i
\(437\) −2.17201 + 8.10604i −0.103901 + 0.387764i
\(438\) −0.778531 + 1.34846i −0.0371997 + 0.0644317i
\(439\) 14.3012 + 24.7704i 0.682559 + 1.18223i 0.974197 + 0.225698i \(0.0724662\pi\)
−0.291639 + 0.956529i \(0.594200\pi\)
\(440\) −3.80467 + 1.01946i −0.181381 + 0.0486008i
\(441\) 0 0
\(442\) 11.4672 34.3065i 0.545437 1.63179i
\(443\) 3.68575 6.38391i 0.175115 0.303309i −0.765086 0.643928i \(-0.777304\pi\)
0.940201 + 0.340620i \(0.110637\pi\)
\(444\) 1.75043 1.75043i 0.0830716 0.0830716i
\(445\) −16.1342 −0.764836
\(446\) 35.7837 1.69441
\(447\) −8.43576 + 8.43576i −0.398998 + 0.398998i
\(448\) 0 0
\(449\) 22.5220 + 6.03476i 1.06288 + 0.284798i 0.747565 0.664189i \(-0.231223\pi\)
0.315315 + 0.948987i \(0.397890\pi\)
\(450\) 1.07878 + 4.02606i 0.0508541 + 0.189790i
\(451\) 2.91077 + 1.68053i 0.137063 + 0.0791332i
\(452\) 6.56704i 0.308887i
\(453\) −0.00601399 + 0.0224445i −0.000282562 + 0.00105454i
\(454\) −22.6558 −1.06329
\(455\) 0 0
\(456\) −3.57364 −0.167351
\(457\) −1.16783 + 4.35841i −0.0546289 + 0.203878i −0.987846 0.155435i \(-0.950322\pi\)
0.933217 + 0.359313i \(0.116989\pi\)
\(458\) 12.0544i 0.563263i
\(459\) −18.4908 10.6757i −0.863076 0.498297i
\(460\) 1.25848 + 4.69671i 0.0586769 + 0.218985i
\(461\) 32.1809 + 8.62285i 1.49882 + 0.401606i 0.912703 0.408623i \(-0.133991\pi\)
0.586112 + 0.810230i \(0.300658\pi\)
\(462\) 0 0
\(463\) 29.0991 29.0991i 1.35235 1.35235i 0.469321 0.883028i \(-0.344499\pi\)
0.883028 0.469321i \(-0.155501\pi\)
\(464\) −36.3047 −1.68540
\(465\) 11.0787 0.513761
\(466\) 27.5016 27.5016i 1.27399 1.27399i
\(467\) −2.85866 + 4.95135i −0.132283 + 0.229121i −0.924556 0.381045i \(-0.875564\pi\)
0.792273 + 0.610167i \(0.208897\pi\)
\(468\) 0.459626 7.55267i 0.0212462 0.349122i
\(469\) 0 0
\(470\) 9.98767 2.67619i 0.460697 0.123443i
\(471\) −2.29227 3.97033i −0.105622 0.182943i
\(472\) 0.507749 0.879447i 0.0233710 0.0404798i
\(473\) −0.219657 + 0.819771i −0.0100998 + 0.0376931i
\(474\) −8.76981 + 8.76981i −0.402811 + 0.402811i
\(475\) 0.696841 2.60065i 0.0319733 0.119326i
\(476\) 0 0
\(477\) −8.20054 14.2038i −0.375477 0.650345i
\(478\) 5.69239 3.28650i 0.260364 0.150321i
\(479\) −23.5643 23.5643i −1.07668 1.07668i −0.996805 0.0798746i \(-0.974548\pi\)
−0.0798746 0.996805i \(-0.525452\pi\)
\(480\) −4.80506 + 2.77420i −0.219320 + 0.126624i
\(481\) 3.45307 + 16.9459i 0.157446 + 0.772665i
\(482\) 5.34507i 0.243461i
\(483\) 0 0
\(484\) 4.06087 7.03363i 0.184585 0.319711i
\(485\) 25.1312i 1.14115i
\(486\) −23.0089 6.16522i −1.04371 0.279660i
\(487\) 14.6038 3.91309i 0.661763 0.177319i 0.0877214 0.996145i \(-0.472041\pi\)
0.574041 + 0.818826i \(0.305375\pi\)
\(488\) 18.3862 + 18.3862i 0.832303 + 0.832303i
\(489\) −7.42080 7.42080i −0.335580 0.335580i
\(490\) 0 0
\(491\) −3.79911 2.19342i −0.171451 0.0989875i 0.411819 0.911266i \(-0.364894\pi\)
−0.583270 + 0.812278i \(0.698227\pi\)
\(492\) 1.70664 + 0.457294i 0.0769415 + 0.0206164i
\(493\) 21.8899 + 37.9144i 0.985871 + 1.70758i
\(494\) −9.36056 + 14.1516i −0.421151 + 0.636713i
\(495\) 4.43238 + 2.55904i 0.199221 + 0.115020i
\(496\) 11.1016 + 41.4317i 0.498476 + 1.86034i
\(497\) 0 0
\(498\) −1.62045 + 0.935569i −0.0726142 + 0.0419238i
\(499\) −19.3575 + 5.18682i −0.866560 + 0.232194i −0.664599 0.747200i \(-0.731398\pi\)
−0.201960 + 0.979394i \(0.564731\pi\)
\(500\) −2.50897 9.36361i −0.112205 0.418753i
\(501\) 1.10963 + 4.14118i 0.0495745 + 0.185014i
\(502\) 19.0940 5.11623i 0.852209 0.228349i
\(503\) −0.917016 + 0.529439i −0.0408877 + 0.0236065i −0.520305 0.853981i \(-0.674182\pi\)
0.479417 + 0.877587i \(0.340848\pi\)
\(504\) 0 0
\(505\) 4.16041 + 15.5268i 0.185136 + 0.690936i
\(506\) −4.25947 2.45920i −0.189356 0.109325i
\(507\) −6.62432 4.98544i −0.294196 0.221411i
\(508\) −3.18576 5.51790i −0.141345 0.244817i
\(509\) −10.8606 2.91008i −0.481387 0.128987i 0.00996149 0.999950i \(-0.496829\pi\)
−0.491348 + 0.870963i \(0.663496\pi\)
\(510\) 11.1386 + 6.43089i 0.493227 + 0.284765i
\(511\) 0 0
\(512\) −1.18017 1.18017i −0.0521565 0.0521565i
\(513\) 7.08184 + 7.08184i 0.312671 + 0.312671i
\(514\) 27.0212 7.24032i 1.19186 0.319357i
\(515\) 20.0748 + 5.37903i 0.884601 + 0.237028i
\(516\) 0.446140i 0.0196402i
\(517\) −1.50646 + 2.60927i −0.0662541 + 0.114755i
\(518\) 0 0
\(519\) 6.06965i 0.266428i
\(520\) 0.878691 14.4388i 0.0385332 0.633185i
\(521\) −14.6510 + 8.45874i −0.641871 + 0.370584i −0.785335 0.619071i \(-0.787509\pi\)
0.143464 + 0.989656i \(0.454176\pi\)
\(522\) 22.4799 + 22.4799i 0.983917 + 0.983917i
\(523\) 0.268849 0.155220i 0.0117560 0.00678731i −0.494111 0.869399i \(-0.664506\pi\)
0.505866 + 0.862612i \(0.331173\pi\)
\(524\) −8.07621 13.9884i −0.352811 0.611086i
\(525\) 0 0
\(526\) −4.12779 + 15.4051i −0.179980 + 0.671695i
\(527\) 36.5750 36.5750i 1.59323 1.59323i
\(528\) 0.804367 3.00194i 0.0350056 0.130643i
\(529\) −7.03308 + 12.1816i −0.305786 + 0.529637i
\(530\) 10.6546 + 18.4543i 0.462806 + 0.801603i
\(531\) −1.27455 + 0.341514i −0.0553106 + 0.0148204i
\(532\) 0 0
\(533\) −9.24224 + 8.18188i −0.400326 + 0.354396i
\(534\) 4.28959 7.42978i 0.185629 0.321518i
\(535\) 18.5526 18.5526i 0.802099 0.802099i
\(536\) −1.71045 −0.0738803
\(537\) −3.83100 −0.165320
\(538\) −0.377635 + 0.377635i −0.0162810 + 0.0162810i
\(539\) 0 0
\(540\) 5.60519 + 1.50190i 0.241209 + 0.0646317i
\(541\) −8.05676 30.0682i −0.346387 1.29273i −0.890984 0.454036i \(-0.849984\pi\)
0.544597 0.838698i \(-0.316683\pi\)
\(542\) 38.9581 + 22.4925i 1.67340 + 0.966135i
\(543\) 3.86450i 0.165842i
\(544\) −6.70465 + 25.0221i −0.287459 + 1.07281i
\(545\) −23.5396 −1.00833
\(546\) 0 0
\(547\) −13.8672 −0.592920 −0.296460 0.955045i \(-0.595806\pi\)
−0.296460 + 0.955045i \(0.595806\pi\)
\(548\) −2.25234 + 8.40583i −0.0962150 + 0.359079i
\(549\) 33.7862i 1.44196i
\(550\) 1.36656 + 0.788983i 0.0582702 + 0.0336423i
\(551\) −5.31504 19.8360i −0.226428 0.845042i
\(552\) 3.67475 + 0.984647i 0.156408 + 0.0419094i
\(553\) 0 0
\(554\) −17.9574 + 17.9574i −0.762936 + 0.762936i
\(555\) −6.14927 −0.261022
\(556\) 13.1846 0.559150
\(557\) −16.0453 + 16.0453i −0.679860 + 0.679860i −0.959968 0.280108i \(-0.909630\pi\)
0.280108 + 0.959968i \(0.409630\pi\)
\(558\) 18.7804 32.5286i 0.795038 1.37705i
\(559\) −2.59959 1.71949i −0.109951 0.0727266i
\(560\) 0 0
\(561\) −3.62003 + 0.969985i −0.152838 + 0.0409528i
\(562\) 6.40703 + 11.0973i 0.270264 + 0.468111i
\(563\) 11.2217 19.4366i 0.472940 0.819156i −0.526580 0.850125i \(-0.676526\pi\)
0.999520 + 0.0309690i \(0.00985932\pi\)
\(564\) −0.409927 + 1.52987i −0.0172610 + 0.0644190i
\(565\) −11.5350 + 11.5350i −0.485283 + 0.485283i
\(566\) 0.777562 2.90190i 0.0326834 0.121976i
\(567\) 0 0
\(568\) −11.6100 20.1090i −0.487143 0.843756i
\(569\) 11.1921 6.46175i 0.469196 0.270891i −0.246707 0.969090i \(-0.579349\pi\)
0.715903 + 0.698200i \(0.246015\pi\)
\(570\) −4.26602 4.26602i −0.178684 0.178684i
\(571\) 15.1053 8.72106i 0.632138 0.364965i −0.149442 0.988771i \(-0.547748\pi\)
0.781580 + 0.623805i \(0.214414\pi\)
\(572\) −1.89880 2.14488i −0.0793928 0.0896821i
\(573\) 13.7928i 0.576202i
\(574\) 0 0
\(575\) −1.43312 + 2.48223i −0.0597650 + 0.103516i
\(576\) 6.93292i 0.288872i
\(577\) 13.9338 + 3.73355i 0.580071 + 0.155430i 0.536912 0.843639i \(-0.319591\pi\)
0.0431598 + 0.999068i \(0.486258\pi\)
\(578\) 30.4813 8.16745i 1.26786 0.339721i
\(579\) 4.37022 + 4.37022i 0.181620 + 0.181620i
\(580\) −8.41357 8.41357i −0.349354 0.349354i
\(581\) 0 0
\(582\) −11.5729 6.68160i −0.479711 0.276961i
\(583\) −5.99760 1.60705i −0.248395 0.0665573i
\(584\) 1.45361 + 2.51772i 0.0601507 + 0.104184i
\(585\) −14.0737 + 12.4590i −0.581874 + 0.515116i
\(586\) 38.4555 + 22.2023i 1.58858 + 0.917167i
\(587\) 4.97130 + 18.5532i 0.205188 + 0.765771i 0.989392 + 0.145268i \(0.0464046\pi\)
−0.784205 + 0.620502i \(0.786929\pi\)
\(588\) 0 0
\(589\) −21.0120 + 12.1313i −0.865783 + 0.499860i
\(590\) 1.65596 0.443713i 0.0681748 0.0182674i
\(591\) −0.764402 2.85279i −0.0314433 0.117348i
\(592\) −6.16199 22.9969i −0.253256 0.945165i
\(593\) −2.51561 + 0.674056i −0.103304 + 0.0276802i −0.310101 0.950704i \(-0.600363\pi\)
0.206797 + 0.978384i \(0.433696\pi\)
\(594\) −5.08337 + 2.93489i −0.208573 + 0.120420i
\(595\) 0 0
\(596\) −3.91804 14.6223i −0.160489 0.598954i
\(597\) 11.9078 + 6.87500i 0.487356 + 0.281375i
\(598\) 13.5246 11.9729i 0.553063 0.489610i
\(599\) −12.4050 21.4861i −0.506855 0.877898i −0.999969 0.00793343i \(-0.997475\pi\)
0.493114 0.869965i \(-0.335859\pi\)
\(600\) −1.17896 0.315903i −0.0481310 0.0128967i
\(601\) 15.2889 + 8.82708i 0.623649 + 0.360064i 0.778288 0.627907i \(-0.216088\pi\)
−0.154639 + 0.987971i \(0.549422\pi\)
\(602\) 0 0
\(603\) 1.57155 + 1.57155i 0.0639987 + 0.0639987i
\(604\) −0.0208490 0.0208490i −0.000848334 0.000848334i
\(605\) −19.4876 + 5.22168i −0.792282 + 0.212291i
\(606\) −8.25620 2.21224i −0.335385 0.0898662i
\(607\) 15.0740i 0.611835i −0.952058 0.305917i \(-0.901037\pi\)
0.952058 0.305917i \(-0.0989631\pi\)
\(608\) 6.07556 10.5232i 0.246397 0.426771i
\(609\) 0 0
\(610\) 43.8969i 1.77733i
\(611\) −7.33438 8.28491i −0.296717 0.335172i
\(612\) 10.8786 6.28074i 0.439740 0.253884i
\(613\) −24.8050 24.8050i −1.00186 1.00186i −0.999998 0.00186450i \(-0.999407\pi\)
−0.00186450 0.999998i \(-0.500593\pi\)
\(614\) 3.17585 1.83358i 0.128167 0.0739972i
\(615\) −2.19449 3.80097i −0.0884904 0.153270i
\(616\) 0 0
\(617\) 9.01921 33.6601i 0.363100 1.35511i −0.506879 0.862017i \(-0.669201\pi\)
0.869979 0.493089i \(-0.164132\pi\)
\(618\) −7.81429 + 7.81429i −0.314337 + 0.314337i
\(619\) −2.05655 + 7.67515i −0.0826597 + 0.308490i −0.994861 0.101253i \(-0.967715\pi\)
0.912201 + 0.409743i \(0.134382\pi\)
\(620\) −7.02896 + 12.1745i −0.282290 + 0.488940i
\(621\) −5.33095 9.23348i −0.213924 0.370527i
\(622\) 47.4915 12.7253i 1.90423 0.510238i
\(623\) 0 0
\(624\) 9.51949 + 6.29663i 0.381084 + 0.252067i
\(625\) −9.64286 + 16.7019i −0.385715 + 0.668077i
\(626\) 33.1665 33.1665i 1.32560 1.32560i
\(627\) 1.75795 0.0702056
\(628\) 5.81741 0.232140
\(629\) −20.3011 + 20.3011i −0.809460 + 0.809460i
\(630\) 0 0
\(631\) 40.9973 + 10.9852i 1.63208 + 0.437314i 0.954517 0.298155i \(-0.0963713\pi\)
0.677559 + 0.735469i \(0.263038\pi\)
\(632\) 5.99339 + 22.3676i 0.238404 + 0.889737i
\(633\) 8.16866 + 4.71618i 0.324675 + 0.187451i
\(634\) 13.1816i 0.523507i
\(635\) −4.09642 + 15.2880i −0.162561 + 0.606687i
\(636\) −3.26404 −0.129428
\(637\) 0 0
\(638\) 12.0357 0.476497
\(639\) −7.80890 + 29.1432i −0.308915 + 1.15289i
\(640\) 26.4076i 1.04385i
\(641\) 17.7415 + 10.2431i 0.700748 + 0.404577i 0.807626 0.589695i \(-0.200752\pi\)
−0.106878 + 0.994272i \(0.534085\pi\)
\(642\) 3.61088 + 13.4760i 0.142510 + 0.531855i
\(643\) −20.9593 5.61604i −0.826556 0.221475i −0.179345 0.983786i \(-0.557398\pi\)
−0.647211 + 0.762311i \(0.724065\pi\)
\(644\) 0 0
\(645\) 0.783647 0.783647i 0.0308561 0.0308561i
\(646\) −28.1676 −1.10824
\(647\) −39.1337 −1.53850 −0.769252 0.638945i \(-0.779371\pi\)
−0.769252 + 0.638945i \(0.779371\pi\)
\(648\) −7.76875 + 7.76875i −0.305185 + 0.305185i
\(649\) −0.249772 + 0.432618i −0.00980440 + 0.0169817i
\(650\) −4.33908 + 3.84126i −0.170193 + 0.150666i
\(651\) 0 0
\(652\) 12.8630 3.44664i 0.503755 0.134981i
\(653\) 14.8092 + 25.6503i 0.579528 + 1.00377i 0.995533 + 0.0944103i \(0.0300966\pi\)
−0.416005 + 0.909362i \(0.636570\pi\)
\(654\) 6.25845 10.8400i 0.244725 0.423876i
\(655\) −10.3848 + 38.7566i −0.405768 + 1.51435i
\(656\) 12.0157 12.0157i 0.469135 0.469135i
\(657\) 0.977702 3.64883i 0.0381438 0.142355i
\(658\) 0 0
\(659\) 1.87682 + 3.25074i 0.0731104 + 0.126631i 0.900263 0.435346i \(-0.143374\pi\)
−0.827153 + 0.561977i \(0.810041\pi\)
\(660\) 0.882106 0.509284i 0.0343359 0.0198239i
\(661\) 30.7260 + 30.7260i 1.19510 + 1.19510i 0.975615 + 0.219487i \(0.0704385\pi\)
0.219487 + 0.975615i \(0.429562\pi\)
\(662\) −23.6341 + 13.6452i −0.918566 + 0.530334i
\(663\) 0.836048 13.7381i 0.0324694 0.533544i
\(664\) 3.49363i 0.135579i
\(665\) 0 0
\(666\) −10.4242 + 18.0552i −0.403928 + 0.699623i
\(667\) 21.8617i 0.846488i
\(668\) −5.25482 1.40802i −0.203315 0.0544781i
\(669\) 13.1517 3.52399i 0.508475 0.136245i
\(670\) −2.04185 2.04185i −0.0788835 0.0788835i
\(671\) −9.04453 9.04453i −0.349160 0.349160i
\(672\) 0 0
\(673\) 23.1880 + 13.3876i 0.893833 + 0.516055i 0.875194 0.483771i \(-0.160733\pi\)
0.0186390 + 0.999826i \(0.494067\pi\)
\(674\) 17.8271 + 4.77675i 0.686673 + 0.183993i
\(675\) 1.71032 + 2.96236i 0.0658303 + 0.114021i
\(676\) 9.68143 4.11651i 0.372363 0.158327i
\(677\) −18.0711 10.4333i −0.694527 0.400985i 0.110779 0.993845i \(-0.464666\pi\)
−0.805306 + 0.592860i \(0.797999\pi\)
\(678\) −2.24506 8.37867i −0.0862209 0.321781i
\(679\) 0 0
\(680\) 20.7971 12.0072i 0.797532 0.460456i
\(681\) −8.32680 + 2.23116i −0.319084 + 0.0854982i
\(682\) −3.68038 13.7354i −0.140929 0.525954i
\(683\) 8.48852 + 31.6796i 0.324804 + 1.21219i 0.914509 + 0.404567i \(0.132578\pi\)
−0.589704 + 0.807619i \(0.700756\pi\)
\(684\) −5.69143 + 1.52501i −0.217617 + 0.0583103i
\(685\) 18.7211 10.8087i 0.715298 0.412977i
\(686\) 0 0
\(687\) −1.18712 4.43039i −0.0452914 0.169030i
\(688\) 3.71593 + 2.14539i 0.141668 + 0.0817923i
\(689\) 12.5801 19.0191i 0.479264 0.724570i
\(690\) 3.21130 + 5.56214i 0.122252 + 0.211747i
\(691\) −43.4491 11.6421i −1.65288 0.442888i −0.692464 0.721453i \(-0.743475\pi\)
−0.960418 + 0.278564i \(0.910141\pi\)
\(692\) −6.67003 3.85094i −0.253556 0.146391i
\(693\) 0 0
\(694\) −5.60257 5.60257i −0.212671 0.212671i
\(695\) −23.1588 23.1588i −0.878463 0.878463i
\(696\) −8.99236 + 2.40950i −0.340855 + 0.0913317i
\(697\) −19.7934 5.30361i −0.749727 0.200889i
\(698\) 38.9298i 1.47352i
\(699\) 7.39940 12.8161i 0.279871 0.484751i
\(700\) 0 0
\(701\) 38.7293i 1.46279i −0.681956 0.731393i \(-0.738871\pi\)
0.681956 0.731393i \(-0.261129\pi\)
\(702\) −4.30417 21.1226i −0.162450 0.797223i
\(703\) 11.6628 6.73352i 0.439871 0.253960i
\(704\) −1.85593 1.85593i −0.0699482 0.0699482i
\(705\) 3.40726 1.96718i 0.128325 0.0740884i
\(706\) −11.0210 19.0889i −0.414780 0.718420i
\(707\) 0 0
\(708\) −0.0679660 + 0.253653i −0.00255432 + 0.00953285i
\(709\) 20.8624 20.8624i 0.783504 0.783504i −0.196917 0.980420i \(-0.563093\pi\)
0.980420 + 0.196917i \(0.0630928\pi\)
\(710\) 10.1457 37.8644i 0.380763 1.42103i
\(711\) 15.0446 26.0580i 0.564215 0.977250i
\(712\) −8.00915 13.8723i −0.300156 0.519885i
\(713\) 24.9490 6.68507i 0.934348 0.250358i
\(714\) 0 0
\(715\) −0.432246 + 7.10276i −0.0161651 + 0.265628i
\(716\) 2.43061 4.20994i 0.0908362 0.157333i
\(717\) 1.76849 1.76849i 0.0660455 0.0660455i
\(718\) −15.7559 −0.588003
\(719\) −8.46228 −0.315590 −0.157795 0.987472i \(-0.550438\pi\)
−0.157795 + 0.987472i \(0.550438\pi\)
\(720\) 18.2970 18.2970i 0.681888 0.681888i
\(721\) 0 0
\(722\) −17.9981 4.82258i −0.669820 0.179478i
\(723\) 0.526386 + 1.96450i 0.0195765 + 0.0730605i
\(724\) −4.24676 2.45187i −0.157830 0.0911229i
\(725\) 7.01385i 0.260488i
\(726\) 2.77656 10.3623i 0.103048 0.384580i
\(727\) 3.27056 0.121299 0.0606493 0.998159i \(-0.480683\pi\)
0.0606493 + 0.998159i \(0.480683\pi\)
\(728\) 0 0
\(729\) 7.45103 0.275964
\(730\) −1.27028 + 4.74076i −0.0470153 + 0.175463i
\(731\) 5.17425i 0.191376i
\(732\) −5.82309 3.36196i −0.215228 0.124262i
\(733\) 3.57318 + 13.3353i 0.131979 + 0.492551i 0.999992 0.00399003i \(-0.00127007\pi\)
−0.868014 + 0.496541i \(0.834603\pi\)
\(734\) −11.8502 3.17526i −0.437400 0.117201i
\(735\) 0 0
\(736\) −9.14692 + 9.14692i −0.337160 + 0.337160i
\(737\) 0.841407 0.0309936
\(738\) −14.8803 −0.547750
\(739\) 30.0608 30.0608i 1.10580 1.10580i 0.112109 0.993696i \(-0.464240\pi\)
0.993696 0.112109i \(-0.0357605\pi\)
\(740\) 3.90146 6.75753i 0.143420 0.248412i
\(741\) −2.04666 + 6.12305i −0.0751861 + 0.224936i
\(742\) 0 0
\(743\) −47.1919 + 12.6450i −1.73130 + 0.463901i −0.980482 0.196606i \(-0.937008\pi\)
−0.750820 + 0.660507i \(0.770341\pi\)
\(744\) 5.49953 + 9.52547i 0.201623 + 0.349221i
\(745\) −18.8021 + 32.5663i −0.688857 + 1.19314i
\(746\) 0.470729 1.75678i 0.0172346 0.0643204i
\(747\) 3.20993 3.20993i 0.117445 0.117445i
\(748\) 1.23083 4.59352i 0.0450036 0.167956i
\(749\) 0 0
\(750\) −6.40223 11.0890i −0.233776 0.404913i
\(751\) 9.96838 5.75525i 0.363751 0.210012i −0.306974 0.951718i \(-0.599316\pi\)
0.670725 + 0.741706i \(0.265983\pi\)
\(752\) 10.7711 + 10.7711i 0.392782 + 0.392782i
\(753\) 6.51387 3.76078i 0.237379 0.137051i
\(754\) −14.0124 + 41.9211i −0.510300 + 1.52668i
\(755\) 0.0732428i 0.00266558i
\(756\) 0 0
\(757\) −8.97468 + 15.5446i −0.326190 + 0.564978i −0.981753 0.190163i \(-0.939098\pi\)
0.655562 + 0.755141i \(0.272432\pi\)
\(758\) 43.6743i 1.58632i
\(759\) −1.80768 0.484368i −0.0656148 0.0175814i
\(760\) −10.8806 + 2.91545i −0.394681 + 0.105754i
\(761\) −7.83029 7.83029i −0.283848 0.283848i 0.550794 0.834641i \(-0.314325\pi\)
−0.834641 + 0.550794i \(0.814325\pi\)
\(762\) −5.95100 5.95100i −0.215582 0.215582i
\(763\) 0 0
\(764\) −15.1571 8.75096i −0.548365 0.316599i
\(765\) −30.1404 8.07610i −1.08973 0.291992i
\(766\) 4.46711 + 7.73726i 0.161403 + 0.279559i
\(767\) −1.21604 1.37364i −0.0439088 0.0495993i
\(768\) −9.20755 5.31598i −0.332249 0.191824i
\(769\) −2.87361 10.7245i −0.103625 0.386734i 0.894561 0.446947i \(-0.147489\pi\)
−0.998186 + 0.0602130i \(0.980822\pi\)
\(770\) 0 0
\(771\) 9.21820 5.32213i 0.331986 0.191672i
\(772\) −7.57523 + 2.02978i −0.272638 + 0.0730533i
\(773\) −0.718001 2.67962i −0.0258247 0.0963792i 0.951811 0.306686i \(-0.0992203\pi\)
−0.977635 + 0.210307i \(0.932554\pi\)
\(774\) −0.972476 3.62933i −0.0349549 0.130454i
\(775\) −8.00436 + 2.14476i −0.287525 + 0.0770421i
\(776\) −21.6079 + 12.4753i −0.775678 + 0.447838i
\(777\) 0 0
\(778\) −1.49192 5.56791i −0.0534879 0.199619i
\(779\) 8.32421 + 4.80599i 0.298246 + 0.172192i
\(780\) 0.746893 + 3.66537i 0.0267431 +